On periodically pendulum-diven systems for underactuated locomotion: A viscoelastic jointed model

This paper investigates the locomotion principles and nonlinear dynamics of the periodically pendulum-driven (PD) systems using the case of a 2-DOF viscoelastic jointed model. As a mechanical system with underactuation degree one, the proposed system has strongly coupled nonlinearities and can be utilized as a potential benchmark for studying complicated PD systems. By mathematical modeling and non-dimensionalization of the physical system, an insight is obtained to the global system dynamics. The proposed 2-DOF viscoelastic jointed model establishes a commendable interconnection between the system dynamics and the periodically actuated force. Subsequently, the periodic locomotion principles of the actuated subsystem are elaborately studied and synthesized with the characteristic of viscoelastic element. Then the analysis of qualitative changes is conducted respectively under the varying excitation amplitude and frequency. Simulation results validate the efficiency and performance of the proposed system comparing with the conventional system.